Tu aurais dû écouter la professeure : sa définition était claire dès le début.

This is the conditional perfect: aurais (conditional of avoir) + dû (past participle of devoir) + the infinitive écouter.

In this sentence, aurais dû écouter means should have listened or ought to have listened.

So:

• tu aurais dû écouter = you should have listened

This structure is very common in French for expressing regret, criticism, or advice about the past:

• Tu aurais dû venir. = You should have come.
• J’aurais dû étudier. = I should have studied.

It often implies that the action did not happen.

Because écouter takes a direct object in French.

In English, we say listen to someone, but in French it is simply:

• écouter quelqu’un
• écouter la radio
• écouter le professeur

So:

• écouter la professeure = to listen to the teacher

This is a very common difference between English and French. Compare:

• regarder quelque chose = to look at/watch something
• chercher quelque chose = to look for something

French often does not use the same preposition that English does.

Dû is the past participle of devoir.

• devoir = to have to / must / to owe
• dû = had to / owed / in this structure, part of should have

Here, it appears in the expression:

• avoir dû = to have had to
• aurais dû = would have had to / should have

The circumflex in dû helps distinguish it from du, which often means some or of the:

• du pain = some bread
• j’ai dû partir = I had to leave

In your sentence, dû is masculine singular because it stays in its default form here.

Both forms exist, depending on region, preference, and level of formality.

• le professeur = the male teacher
• la professeure = the female teacher

In many places, especially in modern standard usage, professeure is a common feminine form. But you may also still see or hear:

• le professeur used for both men and women
• la prof in informal speech

So la professeure is a perfectly normal feminine form meaning the female teacher/professor.

Because définition is a feminine noun, and French possessive adjectives agree with the thing possessed, not with the owner.

So:

• sa définition = her definition / his definition / its definition

Here, sa agrees with définition, which is feminine.

Compare:

• son livre = his/her book (livre is masculine)
• sa définition = his/her definition (définition is feminine)

A common point for English speakers: sa does not mean specifically her. It can mean his, her, or sometimes its, depending on context.

Yes. Sa can mean his, her, or its.

French does not choose son / sa / ses based on the gender of the owner. It chooses them based on the gender and number of the noun that follows.

So:

• sa définition can mean his definition or her definition

In your sentence, because the teacher is la professeure, we understand that sa définition means her definition.

French uses the imparfait (était) here because it describes a state or quality in the past.

• était claire = was clear

The speaker is not focusing on a completed event, but on a description: the definition was clear from the beginning.

If you used a été, it would sound more like a completed event or fact viewed as a whole:

• Sa définition a été claire. = Her definition was clear.

That is possible in some contexts, but était claire feels more natural here because it describes how the definition came across during the explanation.

Because claire agrees with définition, which is feminine singular.

• définition is feminine
• so the adjective must be feminine too:
  • clair → masculine
  • claire → feminine

So:

• un texte clair
• une définition claire

This is standard adjective agreement in French.

Dès le début means from the very beginning or right from the start.

• dès = from, starting at, as early as
• le début = the beginning

So the phrase emphasizes that the definition was clear immediately, not only later.

Compare:

• au début = at the beginning
• depuis le début = since the beginning
• dès le début = from the very beginning / right from the start

This is a very useful distinction.

• dès le début = from the very beginning
• depuis le début = since the beginning

Dès often marks the starting point very sharply.

Examples:

• Dès le début, j’ai compris. = I understood right from the start.
• Je travaille ici depuis le début de l’année. = I’ve been working here since the beginning of the year.

In your sentence, dès le début fits because it means the definition was already clear at the starting point.

The colon introduces an explanation or justification.

So the structure is roughly:

• You should have listened: her definition was clear from the start.

The second part explains why the speaker says the first part.

Also, in French typography, a colon is usually preceded by a space:

• ... professeure : sa définition ...

That spacing is standard in French writing.

Yes.

You could say:

• Vous auriez dû écouter la professeure : sa définition était claire dès le début.

This means the same thing, but with vous instead of tu.

Use tu for:

• friends
• children
• informal situations
• one person you know well

Use vous for:

• one person in a formal situation
• more than one person

So the choice here is about register and who is being addressed.

Yes, a little.

Tu aurais dû écouter... often sounds like:

• You should have listened...
• If you had listened...

So it can express:

• mild criticism
• regret
• a reminder
• frustration

The tone depends on context and intonation. It could be neutral, teasing, or more annoyed.

For example:

• gently: See? You should have listened.
• more sharply: I told you — you should have listened.

A rough pronunciation guide is:

• Tu → like tyu or simply tu
• aurais → roughly oh-ray
• dû → a u sound with rounded lips, not like English doo
• écouter → ay-koo-tay
• la professeure → roughly la pro-fe-sœr

A few points that matter:

• aurais and aurait are often pronounced the same in everyday speech
• dû has the French u sound, which English speakers often find difficult
• professeure ends with a sound like -sœr, not -soor

If you want to sound natural, focus especially on the vowel in dû and on the rhythm of the whole phrase.

Yes, several variations are possible depending on style.

For example:

• Tu aurais dû écouter la prof : sa définition était claire dès le début.
• Tu aurais dû l’écouter : sa définition était claire dès le début.
• Il fallait écouter la professeure : sa définition était claire dès le début.

These are slightly different in tone:

• la prof is more informal
• l’écouter avoids repeating la professeure
• il fallait sounds more general and less directly personal than tu aurais dû

But your original sentence is completely natural and correct.